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Math Help - Finding the trig expression

  1. #1
    Super Member
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    Finding the trig expression

    Hi

    I am having trouble getting the expression for the following:

    1) Write  \frac{tan^2(x)+sec^2(x)}{tanxsec(x)} in terms of sin(x)

    This is what i have done so far:

     \frac{tan^2(x)+(tan^2(x)+1)}{tanxsec(x)}

     \frac{2tan^2(x)+1}{tanxsec(x)}

    This is where i get stuck, what should i do next?

    P.S
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  2. #2
    MHF Contributor
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    Hello Paymemoney
    Quote Originally Posted by Paymemoney View Post
    Hi

    I am having trouble getting the expression for the following:

    1) Write  \frac{tan^2(x)+sec^2(x)}{tanxsec(x)} in terms of sin(x)

    This is what i have done so far:

     \frac{tan^2(x)+(tan^2(x)+1)}{tanxsec(x)}

     \frac{2tan^2(x)+1}{tanxsec(x)}

    This is where i get stuck, what should i do next?

    P.S
    Multiply top-and-bottom by \cos^2x, noting that \tan x = \frac{\sin x}{\cos x} and \sec x = \frac{1}{\cos x} :
     \frac{2\tan^2x+1}{\tan x\sec x}\times\frac{\cos^2x}{\cos^2x}
    =\frac{2\sin^2x+\cos^2x}{\sin x}

    =\frac{\sin^2x+1}{\sin x}
    Grandad
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